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E-raamat: Prolegomenon to Differential Equations and Variational Methods on Graphs

(Delft University of Technology), (California Institute of Technology)
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Prolegomenon to Differential Equations and Variational Methods on GraphsSuurem pilt
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The use of differential equations on graphs as a framework for the mathematical analysis of images emerged about fifteen years ago and since then it has burgeoned, and with applications also to machine learning. The authors have written a bird's eye view of theoretical developments that will enable newcomers to quickly get a flavour of key results and ideas. Additionally, they provide an substantial bibliography which will point readers to where fuller details and other directions can be explored. This title is also available as open access on Cambridge Core.

A bird's eye view of theoretical developments and concrete applications that will enable newcomers to get a flavour of key results. Provides an exhaustive, at the time of writing, bibliography which will point readers to where fuller details and other directions can be explored. This title is also available as open access on Cambridge Core.

Muu info

A bird's eye view of theoretical developments and concrete applications that will enable newcomers to get a flavour of key results.
1. Introduction;
2. History and literature overview;
3. Calculus on
undirected edge-weighted graphs;
4. Directed graphs;
5. The graph
GinzburgLandau functional;
6. Spectrum of the graph Laplacians;
7. Gradient
flow: AllenCahn;
8. MerrimanBenceOsher scheme;
9. Graph curvature and mean
curvature flow;
10. Freezing of AllenCahn, MBO, and mean curvature flow;
11.
Multiclass extensions;
12. Laplacian learning and Poisson learning;
13.
Conclusions; Bibliography.
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